Let me start by saying that as a mechanical engineer I'm definitely not an expert in string or superstring theory! But what I do understand is that these are mathematical constructs that attempt to combine relativity (which applies to "large" objects like planets, space ships, people, and grains of sand) and the physics of extremely tiny subatomic particles, called quantum mechanics. These theories require extra dimensions to be mathematically viable, but often those dimensions only need to exist on a very small scale.
In fact, recent scientific observations suggest that the universe operates in a 3-dimensional space (and only 3 dimensions) for length scales between 1 mile and 80 million light years. See here:
So I believe that these theories are not likely to change travel for people, mostly because we already have a good (if imperfect) understanding of the physics (relativity) that apply to large objects. On the other hand, a better fundamental understanding of how the universe operates can yield surprising advances, possibly revolutionizing things like communication and computing that can happen on smaller scales.
But that is just my opinion, I very well may be wrong about the impact on travel, and a future physicist (maybe you) will be the one to prove it. That's what is really great about science - we always start with opinions and theories, but those theories are always subject to modification when new information becomes available.
It sounds like you definitely have a strong interest in physics, so I'd suggest following up with some additional reading or just have fun with a few Ted Talks: